I have two constant volume gas thermometers, one with an ideal gas p v = R T and the other following the Van der Waals equation ( p + a v 2 ) ( v − b ) = R T. They are calibrated using the freezing point and the boiling point of water. Will they show the same temperatures?

Question

I have two constant volume gas thermometers, one with an ideal gas   p  v  =  R  T and the other following the Van der Waals equation   (  p  +      a          v      2        )  (  v  −  b  )  =  R  T. They are calibrated using the freezing point and the boiling point of water. Will they show the same temperatures?

cenjene9gw · Accepted Answer

Yes they will show the same temperature.For the ideal gas:The temperature as a function of pressure is given by  T  =      V    R    PAs you can see this is a linear graph(V/R is constant). If you calibrate it using water&#039;s boiling and freezing point, and make hundred divisions in the range, you will get accurate values of temperature for a linear change in pressure.For the gas following Van der Waal&#039;s equation:The temperature as a function of pressure is given by  T  =            V      −      b        R    P  +            (      V      −      b      )      a              R              V        2            As you can see this is also a linear function(of the form   T  =  m  P  +  c ). Calibrating this with water&#039;s boiling point and freezing point will give the same temperature readings for linear change in pressure, just as before.

I have two constant volume gas thermometers, one with an ideal gas pv=RT and the other following the Van der Waals equation (p+av2)(v−b)=RT. They are calibrated using the freezing point and the boiling point of water. Will they show the same temperatures?

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